I assume you're using a road bike with 700c wheels? If so, then you plug in 38 as both the largest and smallest chain ring, and 16 as your largest cog, 13 as your smallest. You measured your chainstay length as 42.40 centimeters, and when you generate results you get:

Ring Cog Stay_length Chain_length Gear_inches
1 38 14 42.266 46.5 71.0
2 38 16 42.311 47.0 62.1
3 38 13 42.562 46.5 76.5
4 38 15 42.609 47.0 66.3

This means that none of your gear choices will *exactly* fit your chainstay measurement - note that the stay_length with 38 x 16 is 42.311 and with 38 x 13 and a half-link it's 42.562. 38 x 15 is longer still at 42.609.

Your best bet would be to:

A) Buy a 49t chainring and an 18t cog - that would give you a stay_length of 42.399 and a gear ratio of 71 inches (again assuming you have a 700 x 23c wheel).

B) Buy a 47t or 46t chainring - 47 x 16 would give you a 42.399 stay_length and a 77" gear, and 46 x 15 would also give you a 42.399 stay_length but an even bigger 80" gear (again assuming you have a 700c x blah blah blah).

C) Buy an Eno hub and rebuild your rear wheel or buy a new wheel built around an Eno hub - then use any of those chainrings and cogs you already have, or now have the option to use a lot of different ratios, buy some new chainrings and/or cogs, and find the ideal ratio for your riding style.

craig